Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 8 - Application of Trigonometry - 8.5 Trigonometric (Polar) Form of Complex Numbers: Products and Quotients - 8.5 Exercises - Page 802: 98

Answer

$$13.5747 + 24.4894i$$

Work Step by Step

$$\eqalign{ & \left( {4\operatorname{cis} 19.25^\circ } \right)\left( {7\operatorname{cis} 41.75^\circ } \right) \cr & {\text{Multiply use the product theorem}} \cr & = 4 \times 7\operatorname{cis} \left( {19.25^\circ + 41.75^\circ } \right) \cr & = 28\operatorname{cis} \left( {61^\circ } \right) \cr & {\text{Write in trigonometric form}} \cr & = 28\left[ {\cos 61^\circ + i\sin 61^\circ } \right] \cr & {\text{Use a calculator}} \cr & \approx 13.5747 + 24.4894i \cr} $$
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